Solve Applied Problems Using the Law of Cosines
-Two points $A$ and $B$ are on opposite sides of a building. A surveyor selects a third point $C$ to place a transit. Point $\mathrm { C }$ is 54 feet from point $\mathrm { A }$ and 72 feet from point $B$. The angle $A C B$ is $60 ^ { \circ }$. How far apart are points $A$ and $B$ ?
A) $64.9$ feet
B) $109.5$ feet
C) $78.5$ feet
D) $100.2$ feet

Question

Quizplus · Accepted Answer

Using the Law of Cosines: $AB^2 = AC^2 + BC^2 - 2(AC)(BC)\cos(ACB)$. Substituting the given values: $AB^2 = 54^2 + 72^2 - 2(54)(72)\cos(60^\circ)$. Solving this gives $AB \approx 64.9$ feet.

Solve Applied Problems Using the Law of Cosines -Two Points AAA

Solve Applied Problems Using the Law of Cosines
-Two Points $A$